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128 3. Heterogeneous Processes and Reactor Analysis

h the fractional holdup of the liquid phase
L
D the column diameter
h the fractional holdup of the gas phase
G
h the fractional holdup of solids
S
u the hindered settling velocity of spherical particles
sh
u the terminal settling velocity of spherical particles.
ter
SI units should be used with this correlation.
Another simpler equation is that of Sano et al. (1974; Ramachandran and Chaudhari,
1984; Koide, 1996):

3
kd f p  gu d sG 4 p  0.25 
 13
L
   L  (3.211)
2 0.4
DF 
3   D 
f s L L f
where D is the liquid-phase diffusion coefficient and F is a shape factor and can be taken
f s
as unity for spherical particles.
Liquid–solid interfacial area in slurry r s eactor
By definition, the liquid–solid interf acial area is the total external particle area per unit vol-
ume of bubble-free liquid a , and is gi v en by
c
A l particles,tota
a (3.212)
c
V
L
For spherical particles,
A d n 2 (3.213)
particles,tota l p
d 3
V particle p (3.214)
6
M particles,tota l particle V n p (3.215)

M particles,tota l M l particles,tota
m s V L (3.216)
V m
L s
V particle p n d 3 p n p
V L (3.217)
m m 6
s s

A particle,tota l dn p 2 m 6
a s
c 3 d
V  d n  (3.218)
L p p p p
 
  m 6 s  